asa.other.ass.01

International Indian Statistical Association

Session Slot: 8:30-10:20 Thursday

Estimated Audience Size: 40-60

AudioVisual Request: xxx

Session Title: Inference For Stochastic Processes

This topic provides an interface between stochastic processes and statistical inference. Most stochastic models depend on unknown parameters or other nonparametric quantities such as unknown densities etc. Statistical inference from dependent data is an important and a rapidly growing area of research. This session contains three talks on inference for nonlinear spatial data (S. Lele), minimum Hellinger distance estimation for branching processes (T.N. Sriram) and filtering via estimating functions (A. Thavaneswaran and M.E. Thompson).

Theme Session: No

Applied Session: Yes

Session Organizer: Basawa, Ishwar University of Georgia

Address: Department of Statistics University of Georgia Athens,GA 30602

Phone: 706-542-3309

Fax: 706-542-7069

Email: ishwar@stat.uga.edu

Session Timing: 110 minutes total (Sorry about format):

Opening Remarks by Chair - 5 or 0 minutes First Speaker - 30 minutes (or 25) Second Speaker - 30 minutes Third Speaker - 30 minutes Discussant - 10 minutes (or none) Floor Discusion - 10 minutes (or 5 or 15)

Session Chair: Thompson, Mary E. University of Waterloo

Address: Statistics Dept. University of Waterloo,Waterloo ON Canada N2L 3G1

Phone: 519-885-1211 Ext. 5543

Fax:

Email: methomps@setosa.uwaterloo.ca

1. Modeling and Inference for Nonstationary Spatial Data

Lele, Subhash,   Johns Hopkins University

Address: Department of Biostatistics Johns Hopkins University Baltimore, MD 21205

Phone:

Fax:

Email: slele@welchlink.welch.jhu.edu

Abstract: In modeling and inference for spatial data, it is commonly assumed that the covariance structure is stationary and isotropic, meaning that the covariance between two locations depends only on the distance between them. The non-stationarity in the process is usually modelled through trend or dependence on the spatial covariates. However, as in regression, we seldom know or are aware of all the covariates that should be put into the model. The missing covariates in the trend introduce non-stationarity in the covariance parameter. In spatial statistics, it is commonly assumed that the effect of the missing covariates can be accounted for by the use of the dependence or the neighboring values. Although this is true for the point prediction, it is not true when it comes to coverage properties of the prediction intervals. We introduce a hierarchical model for modelling nonstationarity in the covariances. We use the Monte-Carlo Newton Raphson algorithm for estimation of the parameters. We show how prediction intervals for an observation at a new location can be obtained under this model. The prediction intervals obtained under the hierarchical model are shown to have better coverage properties than the prediction intervals obtained under stationary, isotropic model fitted with the same misspecified trend as the hierarchical model.

2. Minimum Hellinger Distance Eestimation for Supercritical Branching Orocesses

Sriram, T.N.,   University of Georgia

Address: Department of Statistics, University of Georgia Athens, GA 30602

Phone: 706-542-3305

Fax: 706-542-3391

Email: tn@stat.uga.edu

Vidyasankar, A., University of Georgia

Abstract: For supercritical branching processes, suppose we postulate that the probability mass function of the offspring variable belongs to a specified parametric family $\{f_\theta ; \theta \in \Theta\}$. If the postulated model is correct, then one can use the MLE $\hat \theta_{MLE}$ to estimate $\theta$ and it is known that $\hat \theta_{MLE}$ is asymptotically efficient. However, it is also well known that MLEs do not, in general, possess the property of stability under small perturbations in the underlying model. To overcome this deficiency, we propose a minimum Hellinger distance estimator $\hat \theta_{MHD}$. We establish its existence, uniqueness, consistency and derive the limit distribution. It is shown that (a) $\hat \theta_{MHD}$is asymptotically efficient (just as the MLE is) if the postulated model is in fact true and (b) the limit distribution of $\hat \theta_{MHD}$ is not greatly perturbed if the assumed model is only approximately true. Robustness properties pf $\hat \theta_{MHD}$ are also studied.

3. Recent Developments in Filtering Via Estimating Functions

Thavaneswaran, A.,   Department of Statistics University of Manitoba

Address: University of Manitoba Winnipeg Manitoba R3T 2N2, Canada

Phone: 204-474-8984

Fax: 204-474-7621

Email: thavane@ccm.umanitoba.ca

Thompson, Mary E., University of Waterloo

Abstract: Godambe's (1995) theorem is applied to continuous time stochastic processes. Filtering formulas are given for short memory semimartingale models as well as for long memory self similar processes. Superiority of the approach over Kalman filtering with non-Gaussian processes is also discussed in some detail.

List of speakers who are nonmembers: None